Research And Application Of Tree Structure Spatially Varying Coefficient Autoregressive Model

In recent years,with the continuous improvement of various data collection technologies,data acquisition paths has become more diverse and the data types have become more complex.When the data has many features and the relationships between the features are complicated,it is slightly difficult to construct a reliable parametric model,and various assumptions about the model need to be relaxed.Therefore,a class of flexible and efficient machine learning algorithms have been developed and applied,where the decision tree algorithm can be said to be the most representative non-parametric machine learning method,this algorithm has a good ability to interpret the data with a large number of non-linear relationships and interactions,and has low computational complexity.At present,the research focus of trees has turned to the integration with statistical models,many scholars have derived many improved algorithms based on this,especially a kind of tree-based varying coefficient models proposed in recent years.The elements in the spatial region are generally not homogeneous,and the cost of using spatial regression models to explore potential information such as "posi-tion" and "spatial interaction" in the research area is usually higher.From a certain perspective,it can be considered that the characteristics of some spatial individu-als are similar,and then the spatial individuals with "homogeneity" are placed in the same group for analysis and processing,so a natural idea is to consider em-bedding the tree method in the spatial regression model.Therefore,based on the existing research,this paper established two kinds of tree structure spatially vary-ing coefficient models MSMOB(Spatially Model-Based Recursive Partitioning)and MTSVC(Tree-Based Spatially Varying Coefficient),through numerical simulation ex-periments,the accuracy of the function structure of the two models under piecewise constant space-varying effects is investigated,as well as the accuracy of coefficien-t estimation,prediction performance and model complexity in the case of smooth space-varying effects.The simulation results show that the TSVC algorithm allows to consider the mixed situation,shows greater flexibility in exploring the potential data generation process,and also has satisfactory accuracy in approximating contin-uous functions by piecewise form,which has outstanding advantages for the study of spatial non-stationarity.As spatial data contain two basic attributes of spatial correlation and spatial heterogeneity,processing these two properties in a unified framework is of great significance for accurately characterizing and describing spatial relationships.This paper further embeds the established TSVC algorithm in the spatial autoregressive model,and proposed a tree structure spatially varying coefficient autoregressive model,to detect the spatial correlation of response variables while exploring the spatial heterogeneity of the regression relationship,and iterates between estimating the spatial lag parameter for given partition structure and determine the partition structure for given spatial lag parameter to obtain relevant parameter estimates.Finally,the model is used to analyze the spatial change characteristics of the impact of precipitation and temperature on the vegetation coverage index in the Yili area of Xinjiang.The study found that the vegetation coverage index has significant spatial correlation,it can be seen from the visual tree graph that the impact and impact intensity of precipitation and temperature on vegetation coverage index in different observation areas are significantly different,and can determined the specific location of the influence intensity change,which makes the information reflected by the model more comprehensive in practical problems.